$D \Xi$ and $D^* \Xi$ Molecular States from One Boson Exchange

TL;DR

This paper investigates the potential for $D \Xi$ and $D^*\\Xi$ molecular states using a one boson exchange model, predicting possible triply heavy pentaquark-like molecules based on heavy quark symmetry.

Contribution

It introduces a regularized one boson exchange model calibrated with the $X(3872)$ to predict new heavy molecular states, extending to triply heavy pentaquark-like molecules.

Findings

The $J^P=1/2^-$ $D^*\Xi$ system is near binding with a large scattering length.

The $D\Xi$ and $D^*\Xi$ systems are not bound under the model.

Predicted series of triply heavy pentaquark-like molecules.

Abstract

We explore the existence of $D \Xi$ and $D^* \Xi$ molecular states within the one boson exchange model. We regularize the potential derived in this model with a form factor and a cut-off of the order of $1\,{\rm GeV}$. To determine the cut-off, we use the condition that the $X(3872)$ is reproduced as a pole in the $J^{PC} = 1^{++}$ $D^*\bar{D}$ amplitude. From this we find that the $J^P= {\frac{1}{2}}^{-}$ $D^*\,\Xi$ system is on the verge of binding and has an unnaturally large scattering length. For the $J^P= {\frac{1}{2}}^{-}$ $D\,\Xi$ and the $J^P= {\frac{3}{2}}^{-}$ $D^*\,\Xi$ systems the attraction is not enough to form a bound state. From heavy quark symmetry and the quark model we can extend the previous model to the $P \Xi_{QQ}$ and $P^* \Xi_{QQ}$ systems, with $P = D, \bar{B}$, $P^* = D^*, \bar{B}^*$ and $\Xi_{QQ} = \Xi_{cc}, \Xi_{bb}$. In this case we predict a series of triply heavy pentaquark-like molecules.